How do you solve and graph abs((3h+1)/2)<8?

1 Answer
Aug 23, 2017

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

-8 < (3h + 1)/2 < 8

First, multiply each segment of the system of inequalities by color(red)(2) to eliminate the fraction while keeping the system balanced:

color(red)(2) xx -8 < color(red)(2) xx (3h + 1)/2 < color(red)(2) xx 8

-16 < cancel(color(red)(2)) xx (3h + 1)/color(red)(cancel(color(black)(2))) < 16

-16 < 3h + 1 < 16

Next, subtract color(red)(1) from each segment to isolate the h term while keeping the system balanced:

-16 - color(red)(1) < 3h + 1 - color(red)(1) < 16 - color(red)(1)

-17 < 3h + 0 < 15

-17 < 3h < 15

Now, divide each segment by color(red)(3) to solve for h while keeping the system balanced:

-17/color(red)(3) < (3h)/color(red)(3) < 15/color(red)(3)

-17/3 < (color(red)(cancel(color(black)(3)))h)/cancel(color(red)(3)) < 5

-17/3 < h < 5

Or

h > -17/3 and h < 5

Or, in interval notation:

(-17/3, 5)